Conditional Kernel Stein Discrepancy

The paper introduces a Conditional Kernel Stein Discrepancy (CKSD) that extends traditional Kernel Stein Discrepancies to evaluate goodness‑of‑fit for conditional distributions. By employing an operator‑valued kernel on the covariate space, the authors lift unconditional KSDs to settings where only a conditional target model and joint samples are available, covering both smooth manifolds and discrete spaces. They prove that the CKSD statistic vanishes exactly when the conditional model matches the true conditional distribution for almost all covariates, and demonstrate its practical effectiveness through experiments on level, power, and runtime.

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